RA5 : COMBINED LASER – GAMMA EXPERIMENTS K. HOMMA1,2, O. TESILEANU3, Y. ARAI4, S. AOGAKI3, B. D. BOISDEFFRE3, L. D’ALESSI3, I. DANCUS3, D…. [600750]
RA5 : COMBINED LASER – GAMMA EXPERIMENTS
K. HOMMA1,2, O. TESILEANU3, Y. ARAI4, S. AOGAKI3, B. D. BOISDEFFRE3, L. D’ALESSI3, I.
DANCUS3, D. FILIPESCU3, M. HASHIDA5, T. HASEBE1, A. ILDERTON6, Y. IWASHITA4, M.
KANDO7, J. KOGA7, T. KUMITA8, K. MATSUURA1, T. MO RITAKA9, K. NAKAJIMA10, Y.
NAKAMIYA5, C. PETCU3, M. RISCA3, S. SAKABE5, K. SETO3, H. UTSUNOMIYA11, Z. YASIN3
1Graduate School of Science, Hiroshima University, Higashihiroshima, Hiroshima, Japan, E -mail:
[anonimizat] -u.ac.jp E-mail: [anonimizat] -u.ac.jp E-mail:
[anonimizat] -u.ac.jp
2International Center for Zetta -Exawa tt Science and Technology, Ecole Polytechnique
3Extreme Light Infrastructu re – Nuclear Physics (ELI -NP) / Horia Hulubei National Institute for
R&D in Physics and Nuclear Engineering (IFIN -HH), 30 Reactorului St., Bucharest -Magurele, jud.
Ilfov, P.O.B. MG -6, RO -077125, ROMANIA , Email: ovidiu.tesileanu@eli -np.ro E-mail:
sohichiroh.aogaki@eli -np.ro E-mail: bertrand.boisdeffre@eli -np.ro Email: loris.dalessi@eli -np.ro E-
mail: ioan.dancus@eli -np.ro E-mail: dan.filipescu@e li-np.ro E-mail: cristian.petcu@eli -np.ro E-
mail: mihai.risca@eli -np.ro E-mail: keita.seto@eli -np.ro E-mail: zafar.yasin@eli -np.ro
4Institute of Particle and Nuclear Study, High Energy Accelerator Research Organization (KEK), 1 -1
Oho, Tsukuba, Ibaraki, 305 -0801, Japan, E -mail: [anonimizat]
5Institute of Chemical Research, Kyoto University, Gokasho, Uji -city, Kyoto, 611 -001, Japan, E -mail:
[anonimizat] -u.ac.jp E-mail: [anonimizat] -u.ac.jp E-mail:
[anonimizat] -u.ac.jp
6Department of Applied Physics, Chalmers University of Technology, Maskingrand 2, 412 58
Gothenberg, SE -41296, Sweden, E -mail: [anonimizat]
7Quantum Beam Science Directorate, Japan Atomic Energy Agency (JAEA), 8 -1-7, Umemidai,
Kizugawa, Kyoto, 619 -0215, Japan, E -mail: [anonimizat] E-mail
[anonimizat]
8Department of Physics, Tokyo Metropolitan University, 1 -1, Minami -Osawa, Hachioji, Tokyo, 192 –
0397, Japan
9Department of Physics , National Central University , No.300, Jhongda Rd., Jhongli District, Taoyuan
city 32001, Taiwan , E-mail: [anonimizat]
10Center fore Relativistic Laser Science, Institute for Basic Science (IBS), Gwangju 500 -712,
Republic of Korea , E-mail: naka115@dia -net.ne.jp
11 Department of Physics, Konan University, 8 -9-1, Okamoto, Higashi -nada, Kobe, Hyogo, 658 -8501,
Japan E-mail: naka115@dia -net.ne.jp
Abstract. We propose experimental setups in the E7 and E4 experimental areas at ELI -NP
to tackle problems of fundamental physics, taking advantage of the unique configuration and
characteristics of the new research infrastructure to be constructed in Magurele, Romania. The
experimental setups proposed follow a gradual approach from the point of view of complexity, from
the “Day 1” experiments to experiments for which the prerequisites include results from the
previously performed ones . In addition, there are two generic R&D tasks proposed in this TDR,
related to the development of a detection system, Gamma -Polari -Calorimeter (GPC), commonly
2
applicable to energy measurements for electrons, positrons and gamma -rays above the 0.1 GeV
energy scale and the preparatory tests for laser plasma acceleration of electrons up to necessary
energies 210 MeV, 2.5 GeV and 5 GeV for the later stage experiments, respectively.
Key words: High -intensity laser, LINAC based gamma -ray source, productions, iso mers,
photoexcitation, dark matter, 4 -wave mixing, gamma polari -calorimeter, radiation reaction, pair
production, tunneling effects, gamma -gamma collider, and vacuum birefringence
CONTENTS
CONTENTS ………………………….. ………………………….. ………………………….. ………….. 2
GLOSSARY ………………………….. ………………………….. ………………………….. …………. 3
1. INTRODUCTION ………………………….. ………………………….. …………………………. 4
1.1. Stage 1 ………………………….. ………………………….. ………………………….. ………. 8
1.1.1. Production and photoexcitation of isomers at E7 (RA5 -PPEx) ………….. 8
1.1.2. Search for sub -eV Dark Matter candidates at E4 (RA5 -DM) …………… 10
1.1.3. R&D for Gamma -Polari -Calorimeter (RA5 -GPC) …………………………. 12
1.2. Stage 1.5 ………………………….. ………………………….. ………………………….. ….. 14
1.2.1. Radiation Reaction (RA5 -RR) ………………………….. ………………………… 16
1.2.2. The e+e- pair production in the tunneling regime (RA5 -Pair) …………… 16
1.2.3. Polarization properties of Emission in Strong Field (RA5 -Pol) ……….. 17
1.3. Stage 2 ………………………….. ………………………….. ………………………….. …….. 18
1.3.1. All optical table –top - collider at E cms = 1-2 MeV at E4 (RA5 -GG) . 18
1.4. Stage 3 ………………………….. ………………………….. ………………………….. …….. 19
2. PRODUCTION AND PHOTOEXCITATION OF ISOM ERS (RA5 -PPEx) …. 21
2.1. Physics Case ………………………….. ………………………….. …………………………. 21
2.1.1. Photoneutron reaction on nuclei in the ground state ……………………….. 21
2.1.2. Stellar Photoneutron reaction ………………………….. ………………………….. 22
2.1.3. Inducing a nd detecting stellar photoreactions at E7 ……………………….. 23
2.2. Technical proposal ………………………….. ………………………….. ………………… 24
2.3. Estimation Feasibility ………………………….. ………………………….. …………….. 25
3. RADIATION REACTION (RA5 -RR) ………………………….. ………………………… 27
3.1. Introduction/Physi cs Case ………………………….. ………………………….. ………. 27
3.1.1. The Original Model “Lorentz -Abraham -Dirac equation” ………………… 28
3.1.2. The Modern Models of Radiation Reaction ………………………….. ………. 29
3
3.1.3. Remark s for the experiments at ELI -NP ………………………….. …………… 31
3.2. Technical Proposal ………………………….. ………………………….. ………………… 32
3.2.1. Combined 10PW -Laser + GS -LINAC system ………………………….. …… 33
3.3. Estimation o f Count Rate ………………………….. ………………………….. ……….. 35
3.3.1. Models and setup of calculations ………………………….. …………………….. 35
3.3.2. Numerical Result in Stage 1.5 with GS -LINAC ………………………….. … 36
4. E+E- PAIR PRODUCTION IN non-linear REGIME (RA5 -Pair) …………………. 40
4.1. Introduction ………………………….. ………………………….. ………………………….. 40
4.2. Physics case ………………………….. ………………………….. ………………………….. 41
4.3. Technical Proposal ………………………….. ………………………….. ………………… 44
4.4. Count Estimation ………………………….. ………………………….. …………………… 44
5. POLARIZATION PROPERTIES OF EMISSION IN STRONG FIELDS (RA5 –
Pol) ………………………….. ………………………….. ………………………….. …………………….. 45
5.1. Introduction ………………………….. ………………………….. ………………………….. 45
5.2. Physics case ………………………….. ………………………….. ………………………….. 45
5.3. Technical Proposal ………………………….. ………………………….. ………………… 48
5.4. Count Estimation ………………………….. ………………………….. …………………… 48
REFERENCES ………………………….. ………………………….. ………………………….. ……. 48
GLOSSARY
Classification of experiments (code name of experiments in RA5 -TDR)
RA5 -PPEx Experiments of Production and Photoexcitation of isomers (Ch.1)
RA5 -DM Experiments in search of the Dark Matter (Ch.2)
RA5 -GPC R&D of Gamma Polari -Calorimeter (Ch.3)
RA5-RR Experiments of Radiation Reaction (Ch. 4)
RA5 -Pair Experiments of e-e+ Pair production in the tunneling regime (Ch.5)
RA5 -Pol Experiments of Polarization properties (Ch.6)
RA5 -GG Experiments in the Gamma -Gamma Collider (Ch.7)
RA5 -VBir Experiments of Vacuum Birefringence (Ch.8)
AGB Asymptotic Giant Bra nch
ASIC Application Specific Integrated Circuit
CSok Sokolov equation/model in classical dynamics
DAQ Data AQuisition
EFT Effective Field Theory
ELI–NP Extreme Light Infrastructure – Nuclear Physics
FE Front -end Electronics
4
GS Gamma -ray Source
GBS Gamma Beam System
HV High voltage
IC Interaction vacuum Chamber
ID Identification
IM Intensity Monitoring part
LAD Lorentz -Abraham -Dirac equation/model
LBL Light -by-Light scattering
LL Landau -Lifshitz equation/model
LPA Laser Plasma Accelerat ion
LWFA Laser WakeField Acceleration
MC Monte Carlo
MOU Memorandum of Understanding
PMT PhotonMultiplier Tube
QED Quantum ElectroDynamics
QCD Quantum ChromoDynamics
QPS Quasi Parallel colliding System
QSok Sokolov equation/model in quantum dynam ics
RR Radiation Reaction
SPD Single Photon Detection part
SSD Silicon Strip Detector
SZK Seto-Zhang -Koga equation/model
TDR Technical Design Report
WM Wave Mixing part
1. INTRODUCTION
This proposal includes two main topics in physics with staged deve lopments
to gradually tackle them. The first is nuclear reactions, linked to the possibility to
reach, at ELI -NP, conditions encountered in the interior of stars – the production
and photoexcitation of isomers is proposed. The second topic is probing the
photon -photon interactions below the MeV energy scale in general which have not
been explored thoroughly to date by utilizing the laser -laser, laser -gamma and
gamma -gamma collision systems. By these various combinations of photon beams,
we can test sub -eV D ark Matter scenarios as well as nonlinear QED effects both in
perturbative and non -perturbative regimes. It also includes the laser -electron
scattering for the fundamental tests on the radiation mechanisms and pair
production via the tunneling process in e xtremely h igh-intensity laser fields. The
laser -electron experiment also aims at the generation of polarized gamma -rays
from sub -GeV to GeV as probes for the later stage experiments to explore the
vacuum birefringence under high -intensity laser fields. Con sidering a ll of the
above, we define several sections for the experiments performed at E7 and E4
experimental areas (Fig. 1.1 and Fig. 1.2).
We define experimental stages a nd the flow charts depending on the
experimental areas, R&D subjects, and combinations of beam sources necessary
5
for ind ividual experimental proposals i s shown i n Fig. 1.3, where abbreviations L,
e, γ and A corresp ond to laser, electron, gamma -ray beams and nucleus targets,
respectively.
“Stage 1” experiments correspond to technically less difficult proposals
based on available beam sources within the current ELI -NP design .
Fig. 1.1- The Physics cases in RA5 -TDR
6
Fig. 1.2 – The work space for the proposals in RA5 -TDR
At E7, the production of isomers by irradiating MeV electrons produced
with one 1PW/10PW laser line and the excitations with gamma irradiations
(RA5 -PPEx) from the Gamma Beam System (GBS) will be measured via the
observation of neutron emission . Because the expected life times of the isomer
states are larger than millisecond scale , the synchronization iss ue between the
lasers and the GBS is easy to be tackled for this proposal.
At E4, search for weakly coupling sub -eV Dark Matter (RA5 -DM) with
0.1PWx2 and then 1PWx2 will be performed, which is the simplest e xperiment
that utilize s only the laser beams in vacuum chambers.
The prime R&D topic necessary for the following stages 1.5, 3 and 4 is the
development of the common detector, Gamma -Polari -Calorimeter (RA5 -GPC) ,
to measure momenta of e+ and e-, energies of gamma -rays above 0.1 GeV and the
degree of lin ear polarization of gamma -rays via the conversion process to e+e-.
The s econd R&D subject is the generation of 210 MeV, 2.5 GeV and 5.0
GeV electron beams based on Laser Plasma Acceleration (LPA) with gas cel ls for
experimental proposals in the stages 2, 3 and 4. Though we will perform proof -of-
principle experiments at existing infrastructures prior to the operational phase of
ELI-NP, we do not include specific proposals for this subject in our TDR, because
other ELI-NP TDR teams also plan this kind of expe riments and we w ill share the
relevant technical infor mation by the time of commissioning in 2018.
“Stage 1.5” proposals are fundamental tests on radiation reaction (RA5 –
RR), on degrees of linear polarization (RA5 -Pol) and on pair production
(RA5 -Pair) via the tunneling process in extremely high -intensity laser fields by
combining 600MeV electrons from the linac (ELI -NP Gamma Beam System)
and a 10PW laser at E7 . All proposed measurements are possible with the GPC.
These exp eriments can be an alternative pro posal to the E7 -stage -1
experiment (RA5 -PPEx) which shares the common interaction chamber at E7.
Depending on the a dvances of the preparatory experiments relevant to RA5 -PPEx
and on the decision to construct the electron transport line to E7 , the staging o rder
between L(e) + + A (RA5 -PPEx) and e (0.6GeV) + L (RA5 -RR, Pair, Pol) may
be swapped. The stage 1.5 proposals require an additional electron transport line to
the E7 area in order to get the accurately controlled stable electron bunches from
7
the lina c (of the Gamma Beam System ). Also an additional Compton -scattering –
based calibrati on system to synchronize one electron bunch with a 10PW laser
pulse must be in place. The electron bunches will arrive to E7 from the linac with a
lower repetition rate of 1 Hz instead of 100Hz , to reduce the electron current for the
beam dump in E7. Therefore, it is foreseen to guide 1PW laser pulses operated at
1Hz into the E7 area (through the existing 10PW beamlines) which is synchronized
with 10PW with a fixed time differ ence in advance. However, these addi tional
implementations do not pose difficul ties from the technical point of view.
“Stage 2 ” experiment is the realization of an all -optical table -top gamma –
gamma collider at E4 (RA5 -GG) to verify the QED -based elastic ga mma -gamma
scattering. This utilizes the same interaction chamber as that used for RA5 -DM at
E4. This proposal requires 210 MeV electrons by means of laser plasma
acceleration (R&D topic) .
“Stage 3 ” experiments essentially repeat the same measurements as th ose in
the stage 1.5 with upgraded electron energies by means of laser plasma
acceleration. Moreover, we aim at the production of linearly polarized 1 GeV
gamma -ray source via the nonlinear inverse Compton process with 5.0 GeV
electrons for the next stage.
Based on the following basic parameter s for 0.1PW, 1PW and 10PW lasers
and for electrons from GBS LINAC , we briefly introduce in the following sub –
sections the physics cases listed above.
The proposals are summarized in this section , and then details are present ed
for the RA5 -PPEx, RR, Pair and Pol experiments .
Fig. 1.3 – The staged flow charts of the proposals.
Table 1.1
Parameters of the available laser output
Power 0.1 PW 1 PW 10 PW
Pulse energy 2.2 J 22 J 220 J
Pulse duration 22 fsec 22 fsec 22 fsec
Wave length 820 nm 820 nm 820 nm
8
Table 1.2
Parameters of the electron beam from GBS LINAC as used in the proposals
Parameter Value
Energy 600MeV
Bunch charge 4.5-100pC
Number of electrons (avg) 109
Energy spread FWHM 0.1%
Spot size 15
μm
Bunch length 100
μm
Rep. rate of M27 kicking 1 Hz
Divergence 0.5 mm mrad
1.1. Stage 1
1.1.1. Production and photoexcitation of isomers at E7 (RA5 -PPEx)
In this setup, we will investigate the production and photoexcitation of
isomers (RA5 -PPEx) in the E7 area. The interaction chamber , common for all E7
experiments, can be placed either at the crossing point between 10PW laser and
gamma from GS (Figure 1.4) or at the position required by Stage 1.5 experiments
(the choice depends on the adopted neutron detection strategy, to be established in
the preparatory experiments) .
Nuclei in the interior of stars are considered to be in a thermal pho ton bath at
a temperature
T . As a result, nuclei are thermalized in the ground state and excited
states with the thermal population probability expressed by the Boltzmann factor
exp( / )xE kT
, where
xE is the excitation energy and
k the Boltzmann constant.
Therefore, nuclear reactions are induced on excited states in a nucleus as well
as on the ground state under the stellar condition.
For example, in the s-process nucl eosynthesis [1] [Kae11] , the temperature of
the photon bath can be
80.9 10 K in the He intershell and
82.5 10 K in the
thermal pulse phaseof low -mass AGB stars with M < 4M ☼ (solar mass)
and
83.5 10 K in the core He burning , and
91 10 K in the shell C burning of
massive stars with M > M ☼. It can be
9(1.5 3.5) 10 K in the deep O -Ne layers of
massive stars exploding as type I I supernovae in the p -process nucleosynthesis [2-
3] [Arn03,Uts06] .
Nuclear reactions are induced only on the ground state in a nucleus at low
temperature in nuclear l aboratories on earth. We envisage an experimental setup to
induce photoexcitation on an isomeric sta te in a nucleus in the ELI -NP’s E7
experimental area , taking full advantage of the capability of irradiating the nucleus
with extremely intense radiation be ams with different, controlled and highly
accurate photon energies .
9
Figure 1.4 – Experimental setup of E7 -Stage 1
Figure 1.5 – Concept of production and pho toexcitation of an isomer 155Gd with the half -life of 31.97
ms by synchronized irradiations of laser and
-ray beams at E7.
Figure 1.5 depicts a concept of the production and photoexcitat ion of an
isomeric state in 155Gd at 121 keV with the half -life of 32 ms. The 155Gdm isomer is
produced by a single shot of one arm of the 10PW laser (with full or reduced power
at the repetition rate of one shot/minute) or with the 1PW laser at 1Hz repeti tion
rate. The choice depends also on the isomer under study (the latter possibility being
preferable for longer lived states). The laser pulse accelerates electrons at MeV
energies, and then these hit a tungsten target in order to produce Bremsstrahlung
gamma photons that consequently encounter the Gd target. The isomer is photo –
10
excited just above the neutron threshold by a highly -monochromatic
-ray beam
from the GBS under the condition that photoexcitation of the ground state do es not
reach the neutron threshold. Thus, photoexcitation of the isomer is unambiguously
verified by detecting photoneutrons.
Goal of this research: Detecting the photoneutrons resulting from the
interaction of the isomer with the gamma radiation beam fro m GBS.
1.1.2. Search for sub -eV Dark Matter candidates at E4 (RA5 -DM)
In this proposal we search for frequency shifted photons via four -wave
mixing in the vacuum caused by stimulated decay of resonantly produced DM
when two color lasers are combined and focused into the vacuum as illustrated i n
Figure 1.6. Figure 1.7 shows the experimental setup we propose at E4 .
A large fraction of dark components in the universe motivates us to search for
yet undiscovered fields to naturally interpret the relevant observations. Because we
know examples of resonance states coupling to two photons at 126GeV (scalar
field, Higgs) and 135MeV (pseudoscalar field, neutral pion) within only three
orders of magnitude on the mass scale, there might be yet undiscovered similar
types of resonance states over much wider energy ranges in nature, in particular, in
the lower energy side as long as the coupling to two photons is so weak that these
dark fields are not discovered by conventional methods to date. This encourages us
to further search for resonance states at energy ranges below 1MeV that
conventional charged particle colliders will never be able to access. There are
theoretical rationales to expect sub -eV particles such as the axion (pseudoscalar
boson) [4] [Pec97] and the dilaton (scalar boson) [5] [Fuj03] associated with
breaking of fundamental symmetries in the cont ext of particle physics and
cosmology. Therefore, we are led to probe such fields via their coupling to two –
photons in the sub -eV mass range. Furthermore, the advent of high -intensity laser
systems and the rapid leap of the intensity encourage the approach to probe weakly
coupling dark fields with optical photons by the enhanced luminosity factor [6-7]
[Hom12i, Taj12] .
We therefore propose searches for resonantly produce d dark fields with
quasi -parallel two -color laser -laser collider at E4 where 100TW x 2 lasers are
available and 1PW x 2 will also be available if the beam transport at the upstream
is slightly reconfigured .
Goal of this research: Even if no statistically s ignificant four -wave mixing
signal is observed, it is possible to constrain fundamentally important theoretical
models for Dark Matter such as QCD axion scenarios based on the mass -coupling
relation of the exchanged fields as shown in Figure 1.8. The accessible domains by
the searches at ELI -NP are indicated by the two red lines from the top to the
bottom for cases where 0.1PWwith an OPA -based inducing laser and 1PW with an
OPA -based inducing laser are assumed, resp ectively. The assumed data taking
periods are commonly about 10 days. The red lines ind icate that ELI -NP has the
potential to test QCD axi on scenarios in the mass range 1 -100 meV , corresponding
to a sensitivity beyond the present world record.
11
Figure 1.6 – Quasiparallel colliding system(QPS) between two incident photons out of a focused laser
beam with the focal length f, the beam diameter d, and the upper range of incident angles Δϑ
determined by geometric optics. The signature (2−u) ω is produced via the four -wave mixing process,
1ω + 1ω → (2− u) ω + u ω with 0 < u < 1 by mixing two -color waves with di fferent frequencies 1 ω
and u ω in advance at the incidence.
Figure 1.7 – Arrangement of the basic components for the setup and the CAD drawing at E4 to
search for sub -eV Dark Matter via four-wave mixing in the vacuum.
12
Figure 1.8 – Upper limits on the coupling g/m- mass m relation for the scalar field exchange. As
references in Figure 1.8, we put existing upper limits by o ur pilot search (Search at Hiroshima) based
on this method [ 8] [Hom14] and also by the other types of scalar field searches by vertically shaded
areas: the ALPS experiment [ 9][Ehr10] (the sine function part of the sensitivity curve is simplified by
unity for the drawing purpose) which is one of the ”Light Shining through a Wall” (LSW)
experiments, searching for non -Newtonian forces based on the torsion balance techniqu es (Etö -wash
[10] [Abe07], Stanford1 [ 11] [Chi03], Stanford2 [ 12] [Smu05]) and the Casimir force measurement
(Lamoreaux [ 13] [Lam97]). The domains below the vertically shaded areas are all excluded. We note
that if we require the proper polarization combinations between initial and final states for
pseudoscalar fields [ 6] [Hom12p], we will be able to test the QCD axion models in the near future. As
a reference, we show the expected mass -coupling relation based on the QCD axion scenario for E/N =
0 [14] [Ber12a] (KSVZ model [ 15] [Kim79]) which is indicated by the inclining dotted line. The pink
horizontal line indicates the gravitational coupling limit.
1.1.3. R&D for Gamma -Polari -Calorimeter (RA5 -GPC)
Gamma Polari -Calori -meter (GPC) is th e common detector system that will
be employed in Stage 1.5 and 3 at E7 as illustrated in conceptual drawing ( Figure
1.9) and CAD drawing (Figure 1.10).
GPC is designed to be able to measure incident gamma -ray energies from
0.1-5.0 GeV via the conversion process to e+e- pairs and simultaneously measures
the degree of linear polarization. Therefore, a part of GPC also guarantees
capability to m easure momen ta of e+ and e- individually without the gamma –
converter.
Goal of this research: The requirements to this detector system are :
1. momentum resolution with respect to above 100 MeV e+ and e- below 10%.
2. analy zing power to the degree of linea r polarization is greater than 30%.
3. capab ility to m easure more than ten e+e- pairs per shot.
13
Figure 1.9 – Conceptual drawing for Gamma Polari -Calori -meter (GPC). Note that the typical e+e-
opening angle is around sub-mrad. The angle at the top -view is exaggerated.
Figure 1.10 – CAD drawings for GPC
14
Figure 1.11 – Inclusive momentum resolution of produced e+ (closed circle ) and e- (open circle ) above
0.2 GeV.
Figure 1.12 – Analyzing power of gamma -ray polarimetry corresponding to a 50% level. The
amplitude as a function of rotation angles of reaction planes of e+e- pairs around the gamma -ray
incident axis with respect to the polarization plane of the incident gamma -rays reaches 50% (closed
circles) of that of incident 100% linear polarized gamma -rays with 1 GeV (open circles).
Figure 1.11 and Figure 1.12 indicate the inclusive momentum resolution for
e+ and e – above 0.2 GeV, and the analyzing power of polarimetry with respect to
1GeV gamma -rays, respectively .
1.2. Stage 1.5
In this se tup, we will investigate radiation reaction (RA5 -RR), e-e+ pair
production (RA5 -Pair) and polarization (RA5 -Pol) at E7. We can carry out these 3
experiments simultaneously, therefore the considered experimental setup in this
stage is only one configuration (Table 1.3 ). We also investigate the same topics in
15
Stage 3 but employing the multi -GeV electron source produced by LWFA (please
see the configuration Figure 1.16 in Sect. 1.4).
Table 1.3
parameters for experiments
Case Electron
source energy
[MeV] bunch size
[μm] Laser energy
[J] Intensity
[W/cm2] duration
[fs] spot size
[μm]
1 accelerator 600 15 220 (1-2)×1022 22 5.6
2 accelerator 600 15 220 (1-2)×1023 22 1.6
Figure 1.13 – Experimental setup of E7 -Stage 1.5.
16
1.2.1. Radiation Reaction (RA5 -RR)
Radiation reaction (RR) is the first important effect in the interaction between
the ultra -high intens ity laser and a high energetic electron. In the case that an
electron has a high energy, it is predicted that this single electron can emit strong
light by the interaction with ultra -high int ense laser . By u sing lasers at ELI-NP
(10PW – 1022W/cm2 class), all experiments require us to consider RR [16] [Kog04] .
RR represents not only a radiation -feedback effect to an electron motion, but it
describes the characteristics of an electron or how an electron i nteracts with an
external field.
The most basic model was suggested by Dirac, as the Lorentz -Abraham –
Dirac (LAD) equation (1938) [17] [Dir38] . However it in cludes the energy
divergence which is on e of the mathematical difficulties named the run -away
solution. By transformation of the LAD equation, we can find
() dw dt
0 exp( )
. Therefore, many theoreticians have tried to propose a lot of model s for
improvements . For example, the Landau -Lifshitz model is a basic -first order
perturbation of LAD equation [18] [Lan94] . I. Sokolov suggested that radiation
should be described via the total cross section [19-20] [Sok10] . One of the authors
of this TDR, K. Seto considers the LAD model in quantum vacuum for stabilizing
the LAD equation [21-24] [Set14 -1,2 and Set15 -1,2]. Our strong interest is “the
(running) coupling between an electron and high -intense fields” . The current RR
models are based on this idea. We wil l investigate the basic evidences for
establishing the theoretical model of radiation reaction in E7 by using a 10 PW –
1022-23 W/cm2 laser (in Table 1.3 ) and the electron beam of 600MeV from the linac
or over 4GeV from LWFA . The results obtain ed will push f urther the knowledge of
nonlinear/non -perturbative QED treatments .
Goal of this research: Observing the minimum energy of an electron and the
maximum energy of radiation from an electron. The statistic average of them is
equal to the spectrum edge s of rad iation reaction under the condition of Table 1.3
(see also Figure 1.14).
1.2.2. The e+e- pair production in the tunneling regime (RA5 -Pair)
Typical consequence of quantum electrodynamics (QED) is electron -positron
pair production. Especially, pair production only by photons is attractive as a
conversion process between matter and vacuum. There is a long history of
theoretical work on this process from the beginning of QED. However ,
experimental verification is not suffic ient for these theories since it is difficult to
realize the light source energetic enough to produce the electron -positron pairs.
There are several processes to realize the pair production in vacuum. One is
the Breit -Wheeler process derived from perturba tion theory of QED [25] [Bre 34] .
High energy photons interact with each other and are converted into particle pairs.
The threshold is determined by the total energy of the interacting two photons. The
other is spontaneous pair production in a background electromagnetic field [26]
[Sch 51] . This process should be considered in the non -perturbative regime under
the action of numerous photon interactions, which is not demo nstrated compared to
17
the pertu rbative regime. The threshold is determined by the background field
strength and is still far from the available laser intensities.
Fortunately we can approach some part of the non -perturbative regime, i.e.,
strong -field QED, via a combined scheme: interac tion between a strong laser field
and high energy photons [27] [Sch 08] . Detailed cross sections have been obtained
theoretically based on the semi -classical approach. The theory indicates that state –
of-the-art intense lasers c an potentially achieve the near threshold condition of pair
production. Possibility of pair production experiment in ELI -NP is considered to
provide a proof of the strong -field QED.
In this proposal, we consider a simple experimental configuration similar to
that of the previous experiment, SLAC E -144 [28] [bam 99] . The SLAC
experiment is one of the few experimental examples on the pair production in laser
fields. It is shown that SLAC and ELI -NP could approach different regime s of pair
production, being complementary in the exploration of strong -field QED.
Goal of this research: Detection of positrons assuming the laser parameters
in Table 1.3 (see also Figure 1.14).
1.2.3. Polarization prop erties of Emission in Strong Field (RA5 -Pol)
Recent progress of intense laser technology provides new opportunities to
explore the physics of light. One of the most fundamental processes of light is
photon emission from a moving electron. There are two phy sical pictures on this.
One is based on classical electrodynamics. Electrons accelerating under the action
of a background electromagnetic field radiate electromagnetic waves. The other is
based on quantum electrodynamics. The photon and electron interact with each
other and are scattered with the resulting energies. In extremely strong fields, these
two pictures are unified. The quantum emission process becomes nonlinear under
the action of strong background field and electromagnetic waves in classical
radiation are quantized. Theoretical estimations indicate that we could approach the
transition of physical regime from classical to quantum by means of the laser and
electron beam facilities in ELI -NP. In this proposal we focus on the polarization
properties of photon emission in strong fields. While radiated electromagnetic field
in classical regime is highly polarized, the quantum radiation cross section indicate
the emitted photons are depolarized under the influence of spin effects.
Goal of this research : Observing the degree of polarization under the
parameters in Table 1.3 (see also Figure 1.14).
18
Figure 1.14 – Key prediction: the interaction between an initial 6 00MeV electron and 1×1022W/cm2
laser. We observe (1) the scattered electron by RA5 -RR experiment, (2) pair production by RA5 -Pair
experiment and (3) polarization of electron’s radiation by RA5 -Pol experiment, in this Stage 1.5 and
the development of the Ga mma -Polari -Calorimeters (RA5 -GPC) .
1.3. Stage 2
1.3.1. All optical table –top - collider at E cms = 1-2 MeV at E4 (RA5 -GG)
The proposal RA5 -GG aims at observation of real photon – real photon
elastic scattering event for the first time in history as illustrated in Figure 1.15. The
experiment will be performed at
cms1-2MeV E where the cross section is
maximized. For this experiment we need 210 MeV electron beam based on LPA
R&D . This collider can be completely set-up in the interaction chamber used for
the DM search in Figure 1.7.
Figure 1.15 – An all -optical table -top (
3.4 m 1.3 m ) collider: a) top -view including two LPAs
and the detect or system to capture the scattering, b) collision geometry around the
19
interaction point, IP, where -rays are prod uced at each Compton scattering point (CP) in head -on
collisions and
D is the distance between IP and CP.
Goal of this research: We verify the QED -based scattering cross section
by observing large angle scattering events showing clear back -to-back correlated
gamma rays with 0.5 -1.0 MeV as shown in the event display in Figure 1.15. A
three -month data taking period with 0.1PWx2 lasers operated at 10Hz would be
necessary to claim the five sigma statistical significance of such back -to-back
events. Once we c onfirm it, we will shift our focus to search for dark field
resonances around that energy range in general by changing
cmsE . The variable
cmsE
of gamma -gamma collisions by combining laser -plasma accelerated electrons
and the seed laser for Compton scattering to produce gamma rays is the unique
feature of ELI -NP. For this general search, we will use both 2×0.1PW and then 2
×1PW lasers at E4. The series of measurements in the stage 1 and 2 at E4 are
considered to be a general investigation on photon -photon interactions over the
wide energy range from a few MeV down to s ub-eV range.
1.4. Stage 3
In this stage, we repeat the same measurements as those in the stage 1.5,
RA5 -RR/Pair/Pol by upgrading electron energy with laser plasma wakefield
accelerator. Therefore, 10PW lasers will be used and collision geometry will
change from that of the stage 1.5 (Figure 1.16). We consider this stage also as the
preparatory experiments for Stage 4 experiment , namely RR5 -VBir – vacuum
birefringence. To achieve this in Stage 4, we also aim at the genera tion of linearly
polarized gamma -rays around 1 GeV in E7 area. Prerequisites for this experiment
are the results of the demonstrations of LWFA and RR and the generation of
radiation from the interaction between photons and high energy electrons of
0.6GeV, 2.5GeV and 5GeV, respectively .
Table 1.4
parameters for observation
Electron
source energy
[MeV] bunch
size
[μm] Laser
energy
[J] Intensity
[W/cm2] duration
[fs] spot
size
[μm]
case 1 wakefield 2500 15 220 1022 22 5.6
case 2 wakefield 2500 15 220 1023 22 1.6
case 3 wakefield 5000 15 220 1022 22 5.6
case 4 wakefield 5000 15 220 1023 22 1.6
case 5 wakefield 5000 15 22 1021 22 1.6
Goal of this research:
– Observing the minimum energy of an electron and the maximum energy of
radiation from an electron. T he stochastic average of them is equal to the edge
of radiation reaction (RA5 -RR)
20
– Detection of positrons (RA5 -Pair)
– Observing the degree of polarization (RA5 -Pol) assuming the laser parameters
in Tab. 1.4 .
Figure 1.16 – Experimenta l setup of E7 – Stages 3 and 4.
Figure 1.17 – Key prediction: the interaction between an initial 5.0GeV electron and 2×1023W/cm2
laser. We observe (1) the scattered electron by RA 5-RR experiment, (2) pair prod uctions by RA5 -Pair
experiment and (3) polarization of electron’s radiation by RA5 -Pol experiment, in this Stage 3.
21
2. PRODUCTION AND PHOTO EXCITATION OF ISOMER S (RA5 -PPE x)
2.1. Physics Case
2.1.1. Photoneutron reaction on nuclei in the gr ound state
In nuclear astrophysics [3, 29] [Moh00,Uts06] , the reaction rate (
n ), the
number of reactions taking place per unit time, for a photoreaction induced on a
ground -state nucleus leading to the emission of a neutron is given by
0( ) ( )nn cn E E dE
, (2.1)
where c is the speed of light,
n the photoneutron cross sections, and
()nE the
number of photons per unit volume and energy
E . In a stellar interior at a
temperature
T ,
()nE is remar kably close to a black -body or Plank distribution:
2
2311( , )( ) exp( / ) 1En E T dE dEc E kT
. (2.2)
When Eq. (1 .1.2) is substituted for
()nE in Eq. (1 .1.1), the rate becomes a
function of parameter
T . It is then possible to define the photon energy range
which is the most relevant for determining
()nT at the temperature of
astrophysical interest. This results from the properties of the integrand of Eq.
(1.1.1), the product of the photoneutron cross section
()nE and the Planck
distribution
()nE . The in tegrand differs significantly from zero only in a
relatively small energy range defined immediately above neutron threshold. We
call this range the Gamow window for photoneutron reactions. Figure 2.1
illustrates th is Gamow window.
Figure 2.1- The Gamow window for photoneutron reactions defined immediately above neutron
threshold Sn. A narrow energy window is defined as the product of the photoneutron cross section a nd
the Planck distributio n.
22
2.1.2. Stellar Photoneutron reaction
In stellar environments, nuclear excited states are thermally populated. Figure
2.2 depicts photoexcitation on a thermally populated excited state. At high
temperatures, thermalization may enhance the photoreaction rates by several orders
of magnitudes .
The right -hand side of Eq. (1 .1.1), which corresponds to photodisintegration
from the ground state only, must be replaced by a sum of the rates
()nT
for
photodisintegration from all (ground and excited) states
, each term being
weighted by the appropriate Boltzmann factor. Thus, the astrophysical reaction
rate
* is defined by
*
01 2 1( ) ( )exp( / )( ) 2 1nnJT T kTG T J
(2.3)
where
021( ) exp( / )21JG T kTJ
(2.4)
is the temperature -dependent partition function of the target nucleus. Note that in
()nT
,
()nE is replaced by the cross section
()nE for photodisintegration
from state
. Photoexcitation strength function
()XLfE is determined by the
photoabsorption cross section
()XLE summed over all possible spins of the final
states [30] [Cap09] :
21
2()()( ) 2 1L
XL
XLEEfEcL
(2.5)
Here, X represents the electric ( E) or magnetic ( M) excitation mode and L the
multipolarity .
Although nuclear reactions naturally take place not only on the ground state
but also on excited s tates thermally populated in the interior of stars, closed nuclear
systems at high temperatures and densities formed by the gravitational force, they
are induced only on the ground state in experimental laboratories on Earth. As a
result, there is no exper imental information on
()
nE
,
()XLE , and
()XLfE for
any excited state
. Note that
, ( ) ( )total
n XL XL n XL XLE T T E
, where
,XL nT is
the neutron tran smission coefficient and
total
XLT the sum of all particle and radiative
transmission coefficients. Above neutron threshold ( E > S n: neutron separation
energy),
total
XLT is generally dominated by
,XL nT which becomes zero at Sn. Due to a
lack of the experimental information, the Hauser -Feshbach statistical model is used
to calculate
()XLE ,
,XL nT ,
total
XLT , and
()nE
, assuming that the gamma -ray
strength function
()XLfE is the same a s the one for the ground state.
Thus, it is indispensable to experimentally investigate stellar photoreactions in the
laboratory .
23
Figure 2.2– Photexcitation on the excited state .
2.1.3. Inducing and detecting stellar photoreactions at E7
The ELI -NP may become the first research laboratory where stellar
photoreactions are induced and detected. We propose an experiment to induc e
stellar photoreaction at E7 by producing isomers with the high power lasers and
photo -exciting isomers with the intense gamma -ray beam .
The experiments of producing the isomers may be performed either by
multiple laser shots (Type I ) or a single laser sh ot (Type II) of the 10PW lasers. An
isomer is produced in the inelastic electron scattering or in a photoabsorption
reaction, leaving a nucleus in either bound states or unbound states; The bound
states decay to the isomeric state via
-transition [31] [Bel99] , while the unbound
states undergo neutron emission followed by γ-transition to the isomeric state [32]
[Gok06] . Laser -accelerated electrons with kinetic energies of the order of MeV (or
the subsequent Bremsstrahlung radiation) most effectively produce isomers.
Therefore, a key technology is to produce a vast number of MeV electrons by laser
acceleration suited to the production of isomers , by optimizing the operation
condition of the laser with the pulse width of fs .
The Type I experiment is applicable to long -lived isomers with half -lives
sufficiently longer than the frequency (1/60 Hz) of the 10PW laser. The production
of a large number of long -lived isomers is required in the first step followed by
subsequent irradiations with a
-ray beam in the second step to photo -excite the
isomers. In contrast, the Type II experiment is applicable to all isomers irrespective
of their half -lives because isomers are produced by a single laser shot and
simultaneously irradiated with a
-ray beam that is synchronized to the laser shot.
Since the laser shot and the
-ray irradiation are synchronized in a time interval of
the order of ps, the Type II experiment is also applicable to excited state with half –
lives com parable to the synchroniz ation time. The signal -to-noise ratio , limited by
the fact that a relatively small number of isomers are produced by a single laser
shot is greatly improved by applying a short time gate for the synchronized
irradiation of laser an d
-ray beams. A Type II experiment for an isomer 155Gdm
with a half -life of 32 ms is depicted in Figure 1.5. Table 2.1 lists isomers of
research interest .
24
Photoexcitation of isomers is ve rified by detecting photoneutrons. The
155Gdmisomers with the spin -parity of 11/2- and the excitation energy 121 keV are
photo -excited just above the neutron threshold at 6635 keV by a highly
monochromatic
-ray beam with an energ y spread 0.5% (33 keV) in FWHM at
energies between 6314 and 6635 keV. Thus, photoneutron emission occurs on
155Gd not in the ground state but in the isomeric state. The neutron detection is
carried out in collaboration with the research group “Gamma above N eutron
Threshold ”.
Table 2.1
Isomers of research interest
isomers J Ex Half-life
189Osm 9/2- 30.8 keV 5.81 h
180Tam 9- 75.3 keV > 1.2 x 1015 y
176Lum 1- 123 keV 3.66 h
155Gdm 11/2- 121 keV 31.97 ms
152Eum 0- 45.6 keV 9.27 y
115Inm 1/2- 336 keV 2.49 h
113Inm 11/2- 22.4 keV 12.1 y
85Krm 1/2- 305 keV 2.48 h
2.2. Technical proposal
The proposed experiment of the production and photoexcitation of isomers
requires the following preparatory R&D :
1) A preparatory investigation of laser acceleration of electrons with the 1PW laser
at the CETAL facility in Magurele . The peak power (1PW) and pulse width of the
laser need to be modified and optimized to accelerate electrons in the MeV region
at high fluxes . A gas or solid target will be employed for this purpose (th is will be
defined in a common ELI -NP – CETAL research project).
2) Test for the production of isomers with the 1PW laser at the CETAL facility.
Production reactions of the inelastic electron scattering, (e, e’) and (e, e’ n), as
well as photoabsorption o f the Bremsstrahlung gamma ray photons, need to be
investigated with emphasis on the production efficiency of isomers.
The fundamental technology developed by the preparatory investigation will
be applied to the proposed experiment with the 10PW laser and the gamma beam at
the ELI -NP facility. In the E7 experimental area there will be possible to use also
the 1PW laser beam at 1Hz repetition rate, transported through the 10PW
beamline(s). A long focal -length parabolic focusing mirror, housed in a turning bo x
located in the E1/E6 experimental area, will allow for the use of the long focus
(9.5m) at 1PW and 10PW. This is beneficial for electron acceleration in a gas
target, and specifically for this experiment we do not need very tight focus, a long
focal bein g desirable.
25
The electrons accelerated with the help of the high -power laser will hit a first
target, of W, to produce Bremsstrahlung radiation in the gamma domain. Then, at a
distance that depending on the isomer to be studied and on the geometry of the
electron acceleration and Bremsstrahlung setup may vary from a few mm to a few
cm, there is the second target, containing the nucleus of interest. By irradiation
with the Bremsstrahlung gamma rays, part of the nuclei in this target will reach
(directly or i ndirectly) the isomeric state to be investigated.
At a next moment (after a delay depending on the lifetime of the isomeric
state), the target is irradiated with the gamma beam from GBS with an energy
tuned in such a way as to be slightly above the neutron threshold from the isomeric
state (but not also from the ground state) and the photoneutrons are detected.
At ELI -NP there is foreseen a 4 π array for neutron detection, which is
described in the “Gamma above Neutron Threshold” TDR ( Figure 2.3). The
procedures for the purchase of the 3He detectors for this array already started.
Depending on the results of the preparatory experiments, the detectors will be
placed around the secondary (isomer) target, or a fast trans port system will be
installed to transport the target to the 4 π array after the irradiation with the
Bremsstrahlung gamma photons. In either case, the neutron detectors array will be
placed on the gamma radiation beam from GBS (and the photoexcitation of the
isomers created in the target shall occur when the target i s in the detectors array).
2.3. Estimation Feasibility
There are several considerations that support the idea of performing this
experiment at ELI -NP. One of them is the availability of an intense, narrow –
bandwidth gamma radiation beam. Another one is the poss ibility to use high power
lasers for accelerating electrons and put the nuclei in the isomeric states of interest.
The signal to noise ratio for detection is greatly enhanced by the fact that
only a small fraction of the time is covered by the gamma radiat ion pulses, the
macrobunches occupying only 50 μs each second.
Figure 2.3 – Schematic image of the 4π neutron detector structure, proposed in the ELI -NP TDR
“Gamma Above Neutron Threshold”.
26
Figure 2.4 – Spectrum (upper panel) and histogram (lower panel) of the number of Bremsstrahlung
gamma radiation photons exiting the primary W target, function of the angle and energy.
Due to the fact that the production of isomeric states is expected to be more
efficient with the help of gamma photons with respect to electron scattering, there
is envisaged the use of a Bremsstrahlung target placed immediately after the
electron acceleration site (laser beam focus). In Figure 2.4 below there are
displayed the results of the Geant4 simulation of the Bremsstrahlung spectra
originating from a W target on which 106 laser -accelerated electrons arrive with an
energy of 40MeV and an energy spread of 1%.
The number of electrons accelerated with the help of 1PW or 10PW lasers
can be estimated/extrapolated from previous experiments at existing, lower power
lasers [ 33] [Esa09 ]. Thus, a number of 1010 electrons accel erated in the 50MeV
range can be expected from a 1PW laser pulse, while for 10PW this figure may be
one order of magnitude higher.
Considering only the photons exiting the W target at small angles in the
direction of the incident electrons, and imposing an energy threshold above which
photons produce the transfer of nuclei on the isomeric state, one can estimate the
number of isomers produced per laser shot.
Taking as an example the 176Lum case, due to the quite large lifetime of the
isomeric state, several 1PW laser shots can be used in order to excite the target. For
a 1 hour laser functioning, meaning the delivery of 3600 shots at 1PW on target,
27
and assuming a secondary 176Lu target of 1 mm diameter on which consequently
the 8x108ph/s (within the bandwidt h) gamma beam hits, a count rate of about 0.3
neutron/second is expected in the 4 π detector. By using a gate of equal duration
with the time needed for neutron moderation in the polyethylene for each gamma
macro -bunch, the signal to noise ratio is greatly increased (by a factor of more than
103).
For the short -lived isomers, such as 155Gdm (32ms), they can be produced by
one shot of the 10PW laser, then photo -excited by synchronized irradiations with a
single -shot of gamma micro -bunch followed by neutron detection with fast Li glass
scintillation detectors with a time gate 100ns.
The p reparatory experiments of laser acceleration of electrons aim to improve
these numbers by increasing the electron yield and optimizing the geometry of the
setup.
3. RADIATION REACTION (RA5 -RR)
3.1. Introduction/Physics Case
Remarks
The following descriptions of the physics case are partially based on the
recent publication [22] [Set14 -2] by the author of this section . That paper was
intended to propose very brief ly an experimen t for ELI -NP including the
theoretical explanations. And also we extracted the proposal of RA5 -RR from
Technical Design Repor t for Research Activity 5 – Combined Laser and Gamma
Experiments (RA5 -TDR) after adding new information for this present paper .
Ultrahigh intense lasers are being planned and constructed [34] [Mou12]
including ELI-NP [35] [Hab11] . What kind of physical processes can we observe
in the regime of these laser intensities? We often discuss QED effects like pair
creation/annihilation by extreme intensities of 1024~W/cm2 [35] [Hab11] . It has
been predict ed that these lasers will produce new high -field physics. Before
reaching this physical process, we need to pass through the region of 1021~22W/cm2.
In this regime, it is predicted that an electron will emit significant energy as light.
Therefore, the motion of the electron needs to be corrected by the radiation
feedback [16, 36] [Kog04, Zhi01] . This is a basic physical process, named
‘radiation reaction (RR)’. This effect will be appear in the regime of this laser
intensities. All materials have electrons in atoms, and the part of these will be fr eed
from the potential of atoms, then they emit strong light via the interaction with the
high-intensity fields. Therefore, the RR process becomes very important for all
experiments with ultra -intense lasers at intensities over 1022W/cm2.
These intensities are enough reasonable to aim by using ELI -NP’s two 10PW
lasers. In our group RA5 -TDR considers to use E7 experimental area in ELI -NP,
we can use the two 10PW lasers and the LINAC (max 720MeV) for Gamma ray
sources here. By combining these large devices, we intend to carry out to examine
radiation react ion (RA5 -RR), pair creation (RA5 -Pair) , observing polarization of
28
radiation (RA5 -Pol) and vacuum birefringence (RA5 -VBir) under the high –
intensity laser fields. In this chapter , we present the detail of our proposal for the
radiation reaction experiments i n RA5 -TDR (HPLS -TDR3) group , namely the
RA5 -RR experiment.
3.1.1. The Original Model “Lorentz -Abraham -Dirac equation”
Although many readers may indeed argue that this is very obvious and basic
physics, however the RR remains one of the difficult problems in the b asic
equation of an electron’s motion, namely ‘run-away‘ as an instability of its self –
acceleration . The standard theory of it was formulated by Lorentz [37] [Lor06] ,
Abraham [38] [Abr05] and Dirac [17] [Dir38] . Therefore, the equation of a
radiating electron’s motion is named the Lorentz -Abraham -Dirac (LAD) equation.
The easiest way to derive this equation is, from the radi ation energy loss formula
(Larmor’s formula [39] [Lar97] ) in the non -relativistic regime [40, 41] [Jac98,
Pan61] .
2
00
non-relativisticdE dmdt dtv (3.1)
Where,
0m is the electron’s rest mass,
3v
is the velocity of the electron
(
3
is a 3 -dimensional Euclidian space).
c is denoted as the speed of light,
0
23
006e m c
24(10 )
. Therefore, the energy change of an electron is as
follows (
3
exF
is an external field.):
2 2
0
ex 0 02d m dmdt dt vvFv (3.2)
From this equation, we can obtain the equation of motion named the Lorentz –
Abraham (LA) equation.
0 ex LAdmdtvFF (3.3)
2
LA 0 0 2dmdtvF (3.4)
Here, our dynamics is in
initial final[ , ]t t t
with the periodic conditions in
which
initial final initial final( ) ( ), ( ) ( )ddt t t tdt dtvvvv (3.5)
are required. Eq uation (3.4) is the effect of RR, named 'the RR force ‘. Equation
(3.3) with (3.4) was converted to the relativistic regime by Dirac without any
math ematical condition. This is the LAD equation.
0 ex LADdm w eF w fd
(3.6)
22
00
LAD 2 2 2m d w d wf w w wc d d
(3.7)
Where, all of vectors in this equation belong to the 4 -dimensional linear
vector s pace
4
M
joining in Minkowski spacetime
4( , )g
which is the
mathematical set of the 4 -dimensional affine space
4
and the Lorentz metric
g
29
with the signature of
( , , , ) . The force of
4
LAD Mf
is the effect of the
radiation feedback, denoted the RR force.
At first, the LAD theory is de veloped as the electron’s model in classical
dynamics instead of the Dirac equation for avoiding the infinity in QED. After that
it was solved via renormalization [42, 43 and 44] [Tom46, Sch48 and Fey49] , but
he had tried to app ly the Lorentz model (1906) [37] [Lor06] for that . A part of an
electron with the spherical charge distribution interacts with other parts of itself.
But, the field at the center of this charge becomes a singular point (since
2|| rE ,
0 | |r E
). We need to keep in mind that the electron is treated as a point
charge in classical physics. This dependence is taken over the electromagnetic
mass,
0
0
EM 03
4r cmmr
. (3.8)
In the Lorentz’s theory, RR is derived from only the retarded field [45 and 46]
[Lié98 and Wie01] . The equation of electron’s motion (Eq. (3.3) with Eq. (3.4))
becomes
2
0 EM 0 0 2ddm m e mdt dt vvE+ v B . (3.9)
Dirac considered that the infinity of QED is equivalent to the infinity of the
electromagnetic mass [47] [Far09] . In Dirac’s method, he treated not only the
retarded field, bu t also the advanced field [17] [Dir38] . Then, the equation which
he obtained is the LAD equation (3.6) with Eq. (3.7). However, these equations
have a mathematical difficulty which is named “run -away”. For instance, we
consider the case without any external fields. In th is case,
2
0 EM 0 0 2ddm m mdt dt vv
0 EM
000 expd d m m
dt dt m
vv (3.10)
Here,
0 is a very small value with the order of 10-24 sec, the solution grows
up rapidly since
0/ is significant due to the second order derivative
22
00m d dt v
, namely the Schott term. This is the run -away solutio n which we
need to avoid. The same problem is in the LAD equation, too. RR has involved the
history of the single electron model on how to avoid the run -away and the concrete
problem how to estimate this effect under the interactions between ultrahigh –
intensity lasers and highly energetic electrons in many ELI -NP experiments .
3.1.2. The Modern Models of Radiation Reaction
As we discussed above, we need to investigate the method of the solution for
the run -away problem for the estimation of the count -rates for the PW class laser
experiments like ELI -NP. In this small section, we pick up some useful method for
RR researches.
For avoidance of run -away solution, many methods have been proposed and
used for simulations like PIC. The standard method for the avoidance of run-away
was suggested by Eliezer, Ford -O’Connel and Landau -Lifshitz. They considered
the term of the RR force as the higher order corrections. Therefore, the RR force
30
term is treated by the first order of perturbations. By replacing the Schott term
22
0m d w d
with
ex( ) /d eF w d
in the radiation reaction force ,
0 ex ex
0 ex 2( ) ( ) d e d F w d F wm w eF w w w wd c d d
(3.11)
derived by Eliezer [48] [Eli48] and Ford -O’Connel [49] [For93] . For PIC
simulations, the external fields is the function of spacetime,
ex ex ( ( )) F F x
44
MM
. Using the chain rule of derivative in Eq. (3.11), we can obtain the
force of Landau -Lifshitz equation [18] [Lan94] :
2
2 00
0 ex ex ex ex ex ex 24
0d e em w eF w w w F c F F w F F w w wd c c m
(3.12)
Of course,
4
ex Mf
is an external force defined by
ex exf eF w
. Since
this method doesn’t have a run -away due to the absence of the Schott term , it is
useful for the reference of simulations. A scheme similar to this was obtained by
Rohrlich [50] [Roh01] .
Another method which is often used is the Sokolov equation. This is similar to
Landau -Lifshitz equation (3.12), but it is installed the radiation spectrum. For
example, we can obtain the following equations when we choose the classical
radiation spectrum.
cl
ex 22
0dp dx IeF pd d m c
(3.13)
0 ex
00dx p f
d m m
(3.14)
Here,
cl 0 0 ex exI m g f f
means the classical radiation (the Larmor’s formula)
[51] [Sok09] . Then, we consider QED radiation formula
QED cl () I q I with
1
2
5 3 2 3093( ) ( ) ( )8rq dr r dr K r rr K r
, (3.15)
0 C mc
,
2 1 2
0 ex ex 3 2 ( )Cm c g f f
and
(1 ) r r r . This result
was derive d from QED calculation [52, 53]. By using this radiation formula, He
proposed the upgraded equations [ 54] [Sok11] :
QED
ex 22
0I dpeF w pd m c
(3.16)
QED 0 ex
0 cl 0I dx p f
d m I m
(3.17)
Characteristics of this model are, (1) it can realize the main behavior of a
radiating electron by QED -based radiation and (2) the fact that the equations satisfy
the relation
2
0() p p m c
but don’t satisfy
2w w c
. The latter point should be
discussed on the mathematical point of view.
One of the authors in this paper, Seto has also suggested a se ries of new
models, based on the propagation of fields in the QED vacuum fluctuation
proposed by Heisenberg and Euler. By correcting radiation from electron via the
QED vacuum fluctuation (photon -photon scatterings), we can derive the equation,
namely the SZK equation,
31
ex LAD
0 LAD[1 ( )]dew F F wd m f F
(3.18)
22
00
LAD 2 2 2 xxm d w d wF w wec d d
(3.19)
(
2 3 4 3
00 4 / 45 mc
and
( ) |f F F F defined by
|A B A B
) [21-22]
[Set14 -1, Set14 -2]. Then , this equation was upgraded to the “Seto I” model as
follows [23] [Set15 -1]:
dwd d wd
m E F (3.20)
0()[1 ( )] 2!deg g gd m f
EFmF (3.21)
Here,
( ) 7 4 |g F F F and
44
MM F
means the dual tensor of
F . We
should note that
dE and
dm are the measure for the charge and the mass on
the Minkowski spacetime
4( , )g
, satisfying
dE
d d d E m m .
ex LADFFF
and it includes radiation -external field interactions via
LAD ex| FF
and
LAD ex|* FF . In addition, it proceeded the more general model including
QED -based synchrotron formula characterized by Eq. (3.15) (Seto II model [24]
[Set15 -2]):
homdwd d wd
m E F (3.22)
hom hom
22
0 hom hom[1 ( )] ( )2!
[1 ( )] [ ( )]f g g gde
d m f g
FFE
m F F (3.23)
22
00
Mod-LAD 2 2 2( ) ( )
xxm d w d wF w w wec d d
(3.24)
hom ex Mod-LAD FFF
is the homogeneous field. When
QED cl () I I q ,
this set of equations behaves dynamically similar to Eqs. (3.16) – (3.17) [Set15 -2].
These models de monstrated the stability of their solutions, and became good
references.
3.1.3. Remark s for the experiments at ELI -NP
ELI-NP has the potential for carrying out relevant experiments of RR, with
the help of the two 10PW – over 1022W/cm2 class lasers and the GS -LINAC.
Moreover, RR has to be taken into account in all high intensity laser experiments.
The recent models using QED modification show us the running coupling between
an electron and radiation field in high -intens ity fields. There fore, this proposal is
not only about the investigation of the energy loss of a radiating electron, but we
may also observe the running coupling of an electron
dE by high -fields via the
function
)(q [see Eq. (3.15)]. The experiments of RR will give us a chance to
consider not only the problem of laser -electron interactions, but the physics of an
electron model li ke the Dirac’s original prospect.
32
Figure 3.1 – Conceptual layout of RA5 -RR in Stage 1.5. It will be car ried out by the combination of
the 10PW laser and the GS -LINAC .
We propose the experimental geometries of the head -on collision between a
10PW laser beam and 600MeV/2.5GeV/5.0GeV electron s for the RR experiments
in ELI -NP. Figure 3.1 is one of the setup s for RA5 -RR, combining the electrons
from the GBS LINAC (on a n ew transport line to E7) and 10PW laser beam, in
Stage 1.5. We will discuss the technical detail s in Sect. 3.2. This experiment is
based on the observation of two parameters : the minimum energy of scatte red
elect ron/shot and the maximum value of the photon energy. By the correlation of
these two values , one can understand the dynamics of RR.
3.2. Technical Proposal
Before exceeding the numerical results, we provide the experimental setup as
the conclusion of them. From the simulation results, we will classify the models of
radiation reaction (RR) by using a head -on laser -electron interaction. We also use
this setup as the common configuration for RA5 -Pair (Ch.4) and RA5 -Pol ( Ch.5)1
experiments. We need to observe the minimum energy of the scattered electrons
and the maximum energy of the emitted photons from the electron s. The sketch of
this E7 area is Figure 3.2. For this setup, a basic requirement is the synchronization
between the 600MeV electron bunches from the GS -LINAC and the 10 PW laser
pulses, at the sub -ps level. These are also important in the alignment stage of the
setup. In the d evelopment contracts for the 2 × 10 PW laser system and the Gamma
Beam System at ELI -NP, there is already foreseen the possibility of
synchronization at the 100fs level.
In addition, we propose these experiments in E7 -Stage 3 employing LWFA for
2.5/5.0GeV electron beams, to enter another regime of highly intense field physics.
In the following we present the elements that form a functional experimental setup
for this physics case (also for the LWFA case). These elements are also common
equipment for other physics cases proposed in the TDR.
1 We will discuss the physics case of the experiments of RA5 -Pol in Ch. 5. However, t his experiment
can be carried out simultaneously with RA5 -RR.
33
Figure 3.2 -3D layout of RA5 -RR/Pair/Pol experiments in Stage 1.5
3.2.1. Combined 10PW -Laser + GS -LINAC system
In this setup is illustrated in Figure 3.3. We consider to use the electron
bunches from GS -LINAC at M27A magnet in this figure. By using the GS -LINAC,
it is expected a very good beam profile of the electron bunches. Since we consider
to pick up it at the front end of LINAC, the expected electron energy will go up
600-720MeV. Here, we choose 600MeV for an electron’s energy.
We consider th e following setup as the minimum requirement for the
investigations of RR in ELI -NP. By f ollowing the paper of Ref.[ 16, 36]
Ref.[Kog04, Zhi01] , we aim the laser intensity of 1022W/cm2 by the single arm of
10PW laser focusing. The purpose of this experiment is the confirmation of the
theoretical model which we raised at the previous section . Especially, the QED
modification Eqs. (3.15) – (3.17) and (3.22) – (3.24) follow the analysis based on
the Volkov solu tion [55] [Vol35]. This solution assumes that the external field
should be the plane -wave, the strong focusing may violet these models. We select
the f-number of 10PW laser as
#7 f with th e focal length of 3m from this reason.
By this focusing, the spot size is equal to 5.6 μm and the estimated range of the
laser intensity is (1 -2) × 1022W/cm2 depending on the its peak power of 5 -10 PW.
The other parameters of the 10PW laser are basi cally standard parameter in ELI –
NP. The pulse energy, the pulse duration and the laser wavelength are 220J, 22fsec
and 820nm. This PW -class laser enters from E6 area to E7 area and is refracted and
focused by the focusing mirror, finally the beam direction of the delivered laser
should become the same axis of electron bunches extracted from the GS -LINAC
line. (see Figure 3.3)
34
Figure 3.3–Combined 10PW -Laser and GS -LINAC system
We propose the following design for the electron beam. For the observations
of RR, it requires the electron energy of 600MeV with the reputation rate at M27A
magnet on 1Hz -operation. This reputation rate addresses the radiation safeties. The
charge in the bunch is estimated the range of 4.5 – 100pC with the 109-10 electrons
and t he bunch width of 100 μm. Due to the statistic of the scattering processes, it
requires a well -focused electron beam at the interaction point. We propose it as
15μm extracting the LINAC property. Depending on the design of the extraction
line from M27A magnet, we have the optio ns of the additional accelerator modules
for reaching to the electron’s energy of 1GeV.
Then the important problem must be the synchronization between 10PW
laser and the LINAC electron bunches. From the facility side of ELI -NP, we
prepare the synchronizati on system in both by an electronic control. However, we
need to align the electron beam profiles for the precise experimental trials. From
these reason, we also propose the optical synchronization/alignment system in E7
area. There are two arms of 10PW las ers in E7 area. Here, we use the rest laser line
for these synchronization and alignment. Though the M27A magnet in LINAC line
is operated at 1Hz bunch kicking, the laser for them should be also operated at 1Hz,
too. Avoiding the amplification from 1PW to 10PW, we can use the 1PW -1Hz
operation in E7 area, theoretically. A part of this 1PW in E7 area, it is used for
making 90 degree Compton scattering with electron bunches from LINAC. The
two arms of lasers should be synchronized, we can manage the time matc hing
between 10PW -main laser and LINAC by using this scheme. During the time
matching, we lead the rest part of 1PW – 1Hz operated laser to the opposite
direction of the electron bunches, make the experimental geometry of the head -on
collisions for scannin g the electron beam profile. The final focusing mirror for it
locates at the movable -controllable table, we can obtain the electron beam profile
by automatically sliding this table.
35
3.3. Estimation of Count Rate
3.3.1. Models and setup of calculations
In RA5 -RR, the most interesting point is the choice of appropriate RR model
in the regime of ELI -NP. Table 5. 1 is the list of models which we consider in the
present phase, the w here symbols LL, CSok, QSok , SZK and Seto II stand for
Landau -Lifshitz [18] [Lan94] , Sokolov (classical) [51] [Sok09] , Sokolov
(quantum) [ 54] [Sok1 1], Seto -Zhang -Koga models [ 21] [Set14 -1] and the Seto II
model [ 24] [Set15 -2] respectively. We have p erformed numerical simulations for
tracking a radiating electron and the radiation spectrum in order to evaluate the
model dependency of laser -beam interaction s. In the spectrum estimation, the
quantum emission spectrum [52] [Nik64] is employed for SQ and Seto II model s
while the classical emission spectrum [40] [Jac98] is used for the other models.
We consider the following combined laser and LINAC experiments: the peak
intensity of the laser is
I
1.0
2210
2W / cm by spot size
PS
5.6
μm for 5PW
with pulse duration
22 fsecPT and wavelength
820 nm . The i ncident
electron energ y is
E 600 MeV provided by LINAC . Figure 3.4 is a diagram
illustrating the configuration of electron scattering along with the definition of
relevant angles: electron incident angle
L , electron scattering angle
e , and
photon detection angle
.
Table 5. 1
Models of RR
Model name Equation
Landau -Lifshitz
[LL],
Eq. (3.12)
0
0 ex ex 2
2
2 0
ex ex ex ex 4
0()dem w eF w w w Fdc
ec F F w F F w w wcm
Sokolov (classical)
[CSok],
Eqs. (3.13)-(3.14)
cl
ex 0 ex 22
00()dp e Ig F p f pd m m c
Sokolov (quantum)
[QSok],
Eqs. (3.16)-(3.17)
cl
ex 0 ex 22
00([( ) ]) dp e q Ig F p q f pd m m c
Seto-Zhang -Koga
[SZK],
Eqs.(3.18)-(3.19)
ex LAD
0 LAD()[1 ( )]dew F F wd m f F
Seto II
[Seto II]
Eqs.(3.22)-(3.24)
hom hom
hom hom
22
0 hom hom[1 ( )]
()
[1 ( )] [ ( )]f
g dw ewd m f g
FF
FF
FF
36
Figure 3.4 – Configuration of an electron scattering by a pulse laser.
3.3.2. Numerical Result in Stage 1.5 with GS -LINAC
We consider the case of the laser intensity of 1 ×1022 W/cm2 by focusing the
peak power of 5 PW and the electron energy of 600MeV by using the GS LINAC
line.
Figure 3.5 and Figure 3.6 show the electro n orbits and the time evolution of
electron energy calculated based on SZK, LL, CSok, QSok and Seto II models.
Here, the case of the head -on collision, i.e.,
0L
, is considered. As shown in
Figure 3.5, the incident electron starts to oscillate under the action of laser
electromagnetic field as it approaches the pulse laser. The electron tends to
decelerate toward the directi on of laser propagation (
x direction) during the
oscillation by light pressure. The e lectron eventually exhibits different dynamics
according to the employed RR model and passes away into the distance with a
certain scattering ang le. As shown in Figure 3.6, the electron energy decreases
drastically due to RR during the oscillation phase. The asymptotic value of electron
energy considerably depends on the employed RR models. Scattered electr on
energy is estimated for various beam incident angles
L . We recognize two model
group s from the final energies of an electron. The three models of LL, CSok and
SZK are overlapped each other. And also QSok and Seto II are overlap ped.
Figure 3.7 shows the scattered electron energy as a function of incident
electron angle for each RR model. The e lectron energy decreases considerably
from the initial beam energy, 600 [MeV], due to radiation d amping in any incident
angles. Typical electron energy loss ranges from ~ 300 [MeV] for QSok and Seto II
model to ~ 400 [MeV] for LL model. Therefore evidence of RR could be observed
from the scattered electron energy. In addition, dependency of scattered electron
energy on RR model becomes obvious as th e incident angle becomes large.
37
Figure 3.8 shows electron scattering angle estimated for various incident
angles. The i ncident electron energy in the present case is large enough so that the
electrons pass thr ough the pulse laser without significant deflections.
Figure 3.5 – Trajectory of a 600MeV electron head -on colliding with the 1×1022W/cm2 laser pulse.
38
Figure 3.6 – Time evolution of electron energy . An electron of the initial energy of 600MeV head -on
collides with the 1×1022W/cm2 laser pulse. Due to radiation from an electron, we can find the energy
drop of it and it represents the effect of RR.
39
Figure 3.7 – Scattered electron e nergy vs. laser incident angle vs. laser incident angle.
Figure 3.8 – Electron scatter ing angle vs. laser incident angle .
Figure 3.9 – Angular distributions of emitted photon energy in the case of the 1×1022W/cm2 laser and
a 600MeV electron. The calculation resolution of the detection angle is dθ=2π/211.
40
Returning to the topic of the head -on collision case
0L , Figure 3.9 shows
angle distribution of photon energy per one incident beam electron. This
calculation was carried out by using the angular resolution
1122 d . Emitted
photon energy is confined to small angles around the beam front direction,
0
because parallel emission is dominant for high -energy electron [the spread angle of
radiation is
21
electron 0~ ( / )d E m c , strong directivity]. The emission angle
distribution broadens up to
5 – 10
, which is wider than the angle
distribution of scattered electron. This is because photon emission from oscillating
electron directly contributes to the emission angle distribution. Thus, the emission
spectrum measurement might provide an excellent indication for the model
dependency of RR.
Please see Chapter 5 about the proper ties of the polarized and depolarized
radiation .
4. E+E- PAIR PRODUCTION IN NON -LINEAR REGIME (RA5 -PAIR)
4.1. Introduction
Typical consequence of quantum electrodynamics (QED) is electron -positron
pair production. Especially, pair production only by photons is attractive as a
conversion process between matter s and vacuum. There is a long his tory of
theoretical work on this process from the beginning of QED. However
experimental verification is not sufficient for these theories since it is difficult to
realize the light source with enough energy to produce the electron -positron pairs.
There a re several processes to realize the pair production in vacuum. One is the
Breit -Wheeler process derived from perturbati on theory of QED [25] [Bre 34] .
High -energy photons interact with each other and are converted into particle pairs.
The threshold is determined by the total energy of the interacting two photons. The
other is spontaneous pair production in a background electromagnetic field [26]
[Sch 51] . This process should be considered in the non -perturbative regime under
the action of numerous photon interactions, which is not understood compared to
the perturbative regime. The threshold is determined by the background field
strength and is still far from the available laser intensities.
Fortunate ly we can approach some part of the non -perturbative regime, i.e.,
strong -field QED, via a combined scheme: interaction between a strong l aser field
and high -energy photons [27] [Sch 08] . Detailed cross sections have been obtai ned
theoretically based on the semi -classical approach. The theory indicates that state –
of-the-art intense lasers can potentially achieve the near threshold condition of pa ir
production. Possible pair production experiment in ELI -NP is considered to
provid e a proof of the strong -field QED.
In this proposal, we consider a simple experimental configuration similar to that of
the previous experiment, SLAC E -144 [28] [bam 99] . The SLAC experiment is one
of the few experimental exam ples on the pair production in laser fields. It is shown
that SLAC and ELI -NP could approach different regimes of pair production, being
complementary in the exploration of strong -field QED.
41
4.2. Physics case
We describe several pictures of pair production in v acuum and their relevance
to the present experiment in ELI -NP. Perturbation theory of QED derives pair
production due to collision of two energetic photons. This is called Breit -Wheeler
(BW) pair production [25] [Bre 34] . Field energy associated with its strength also
becomes an energy source of particle pair. Low frequency and strong field limit
suggests spontaneous pair production from a constant but intense electromagnetic
field [26 56] [Sau 31, Sch 51] . In the framework of QED, this process is regarded
as a pair production from numerous low energy photons interacting simultaneously.
Pair production in strong field is therefore not fully explored since non -perturbative
treatment is required.
The spontaneous pair production is illustrated as a tunneling process in vacuum.
Particles in the negative energy region can pass through the steep potential
structure of background field by tunneling effect to reach the positive ene rgy
region. Probability of the tunneling process is estimated by using a typical electric
field, i.e., Schwinger field
2~SE mc e , where
denotes Compton wavelength.
Resulting probability,
SP , is given as
expS
SEPE (4.1)
stand s for the strength of background elect ric field [26] [Sch 51] . The exponential
dependency is a consequence of the tunneling effect.
Figure 4.1 shows typical diagrams of the pair production from high -energy
photons. Panels ( A) and (B) indicate single -photon and multi -photon BW processes
[57] [Rei 62] , respectively. Threshold of single -photon BW process is determined
by total photon energy in the center of mass system (CMS) of generated particle
pair. The characteristic parameter,
is
2, 4 , 4th
th Lss mc ss (4.2)
where
ths and
s are the minimum energy required for pair production and total
photon energy in CMS, respectively.
and
L are photon energies. Head -on
collision is assumed here. Threshold of single photon BW process is given by
1
. For sub threshold case
1 , particle pair can be generated only via multi –
photon BH process. If additional photons come from a laser field, minimum
number of interacting photon to produce one particle pair,
minN , is estimated by
2
min~ (1 a ),
LeENamc (4.3)
where a is normalized vector potential of laser and
L is now laser frequency [28]
[Bam 99] . Required photon energy is quite large for singl e BW process in laser
fields since laser frequency is small. For example, minimum photon energy is ~
100 [GeV] for laser energy ~ 1 [eV].
42
Figure 4.1 – Diagrams of typical pair production processes involving energetic photons. (A) single –
photon BW process. Two photons γ1 and γ2 interact each other. (B) multi -photon BW process. N
photons γ1 … γ2 interact each other. (C) Pair production from energetic photon γh in strong field.
Double lines indicate dressed particle
Figure 4.1 (C) represents pair production in strong field. Double lines stand
for dressed e lectrons (or positrons) interacting with vast number of photons in
external field [58] [Fur 51] . Although the pair production is essentially non –
pertu rbative, semi -classical approach can be applied for pair production triggered
by an energetic photon in strong -field – stimulated pair production. Contribution of
external field is exactly included in the dynamics of dressed particles [52, 55] [Vol
35, Nik 64] and perturbative interaction is considered between the energetic photon
and the dressed particles. Photon interaction in semi -classical regime is
characterized by the quantum parameter
,
2
22()LLef f F pmc mc mc
(4.4)
where
,
F and
p denote Compton wavelength, field 4 -tensor and 4 –
momentum of photon, respectively. Pair production cross section,
( , )pairW , is
then
24
2 3 1 3( , )()
3pair
hdW mcK ds K sd h
(4.5)
where
,
h and
h are fine structure a nd Plank constants and photon energy,
respectively.
() denotes ratio of positron (electron) energies to photon energy,
i.e.,
eh and
1 .
is defined by
2 3 1 [52, 59] [Ber
81, Nik 64] . Total cross section grows exponentially for
~1 . Probability of pair
production is roughly estimated as [60] [Nar 68] ,
81exp3P (4.6)
This formulation invokes the tunneling effects as in the spontaneous pair
production however the probability is determined by
, not
SEE .
We consider the relevance of above mentioned pair production processes t o the
experiments in ELI -NP [61] [Ion 14] while comparing that in SLAC E -144 [28]
[Bam 99] experiment. Experimental parameters are summarized in Table 4.1 (left
three columns: electron energy, number of electron per bunch and laser intensity
43
(normalized potential). For ELI -NP, we consider two types of electron bunch. One
is electron bunch from LINAC with energy of 600 [MeV]. The other is generated
via laser w akefield acceleration. Considered electron energy is 2500 [MeV] [62]
[Nak 14] . Energy range of seed photon (the forth column) is roughly estimated by
the energy spectrum of photon emitted from the incident electron bunch
(experimental data for SLAC and simulation date for ELI -NP).
We estimate three typical parameters characterizing above -mentioned three
pair production processes. Head -on collision between seed photon and pulse laser
is assumed here. The first parameter
SEE on spontaneous pair production
[Eq.(4.1)] is quite small ( < 10-3) even for ELI -NP as shown in the fifth column.
Therefore spontaneous pai r production is still negligible. The second parameter
minN
in the sixth column is required photon number in multi -photon BW process
[Eq.(4.3)].
minM is quite different between ELI -NP (~105-6) and SLAC (~5). This
estimation indicates that pair production could take place only in highly non –
perturbative regime in ELI -NP while multi -photon process with a few photons i s
dominant in SLAC.
Despite this large difference of physical regime, the quantum parameter [Eq.
(4.4)] in ELI -NP (600 MeV LINAC) has a value relatively clos e to that in SLAC,
as shown in the seventh column. The quantum parameter is here estimated by
2( )( )sE E E mc
, where
E is seed photon energy . Thus similar pair
production rate is expected in strong field QED under the contribution of different
number of laser photons.
Finally, generated positron number per electron bunch is given in the eighth
column (Observed positron number for SLAC and simulation results for ELI -NP).
The simulation is based on the cross section desc ribed in Eq. (4.5). The e xpected
positron number for 600[MeV] electron beam is similar to the result of SLAC, as
indicated in the quantum parameter. For 2.5[G eV] case, the positron number
increases significantly (>104) compared to the other cases. This is a consequence of
the exponential growth of pair production probability as in Eq. (4.6). Precise
measurements of pair production rate and careful comparison with the result of
SLAC experiment could provide a proof of the strong field QED.
Table 4.1
Parameters of the ava ilable laser output
44
4.3. Technical Proposal
The requirements and the experimental setup are identical to the ones for the
experiments of radiation reaction, without any difference. For observing the e-e+
pairs, removing the beryllium window as the
-pairs converter (GPC).
4.4. Count Estimation
We estimate the pair production rate in the collision between electron beam
and intense pulse laser. The estimation is based on a numerical simulation
employing the cross sections of radiation and pair production. The cross sections
are,
2
5 3 2 3( , ) 1( ) 1 2 ( )1 3rad e
e
eedW mcdsK s Kd
24
2 3 1 3( , )( ) ( )
3pair
hdW mcK dsK sd
(4.7)
where
radW and
pairW are the cross section of radiation and pair production,
respectively.
,
e and
() are the quantum parame ter, ratio of emitted photon
energy to incident electron energy and ratio of positron (electron) energy to
incident photon energy, respectively. δ is defined as
2 3 [(1 ) ]ee for
radiation and
2 3 1 ( ) for pair production.
The e xperimental configuration is the same as that in RA5 -RR. The
primary process is again high -energy photon emission and its back reaction of
electrons. The pair production is seeded by the emitted photons. That is, the pair
production takes place as a two -step process,
(1)
(2)LL
hLe N e
N e e
(4.8)
where
h ,
L and
N denote high energy photon, laser photon and absorbed
number of laser photon, respectively. In the present situation, particle pair is also
generated via direct interaction between electron and laser field witho ut high –
energy real photon (trident pair production) [15, 63-64] [Ild 11, Hu 1 0, Kin 13] .
Probability of this process is expected to be q uite small compared to the two -step
process. Thus this process is neglected in the simulation.
Physical condition considered for the simulations are as explained in RA5 -RR.
Laser intensity, pulse duration, spot size are 1022 [W/cm2], 22 [fs] and 5[um],
respectively. Electron beam is obtained from accelerator and typical energy is 600
[MeV]. The other is obtained by using plasma wake field acceleration and energy
is 2500 [MeV].
Figure 4.2 shows the simulation res ults. The lines indicate energy spectrum of
emitted photon, absorbed photon and generated positron. In this case, the quantum
parameter is not so large (< 0.25,). Thus only small fractions of high -energy
photons with energies of ~200 -450 [MeV] are absorbed in the laser field, as shown
in the purple line. Positron energy is roughly half of the absorbed photon energy,
i.e., ~ 100 -300 [MeV]. Total number of positron per one electron beam (109
incident electrons) are ~ 1.
45
Figure 4.2 – Energy spectrum of emitted photon, absorbed photon and generated positron.
Electron beam energy is 600 [MeV]. Energy bin size is 10 [MeV].
5. POLARIZATION PROPERT IES OF EMISSION IN S TRONG FIELDS
(RA5 -POL)
5.1. Introduction
Recent progress of intense laser technology provides new opportunities to
explore the physics of li ght. One of the most fundamental processes of light is
photon emission from a moving electron. There are two physical pictures on this.
One is based on classical electrodynamics. Electrons accelerating under the action
of a background electromagnetic field radiate electromagnetic waves. The other is
based on quantum electrodynamics. The photon and electron interact with each
other and are scattered with the resulting energies. In extremely strong fields, these
two pictures are unified. The quantum emission process becomes nonlinear under
the action of strong background field and electromagnetic waves in classical
radiation are quantized. Theoretical estimations indicate that we could approach the
transition of physical regime from classical to quantum by mea ns of the laser and
electron beam facilities in ELI -NP. In this proposal we focus on the polarization
properties of photon emission in strong fields. While radiated electromagnetic field
in classical regime is highly polarized, the quantum radiation cross section indicate
the emitted photons tend to be depolarized under the influence of spin effects.
5.2. Physics case
Classical treatment of radiation is based on the Liénard -Wiechert potential
generated by a moving charged particle. In highly relativistic electro ns,
synchrotron radiation can be applied to radiation processes in arbitrary
electromagnetic fields [40] [Jac 99] . Resulting angle distribution and frequency
spectrum are
46
2 2 2 2 2 2 2 2 2
0 2 3 0 1 3(1 ) ( ), (1 ) ( )dI dII K I Kd d d d
22
2 2 3 2
0 231(1 )42cceIc
(5.1)
Where
I and
I
are parallel and perpe ndicular polarized components of emission
intensity. Here
,
and
denote gamma factor of emitting electron, frequency
and angle of emitted photon, respectively.
is solid angle of radiation.
#K is the
MacDonald function. Characteristic frequency
c is given by
3
2c L L c f f (5.2)
where
Lf denotes the Lorentz 4 -force. By integrating with respect to
and
,
radiation spectrum and total radiation intensity are obtained as,
()c
cc
ccdIIQd
2
53 239 3 2( ) ( ),83LL
cre f fQ r dx K x Imc (5.3)
where
cI corresponds to the total radiation intensity. At least for low energy
emission, synchrotron radiation is theoretically well established and has lots of
technological applications and releva nce to astronomical phenomena. Hereinafter,
“classical cross section” is used for the synchrotron cross section, Eqs. (5.1) and
(5.3).
Radiation process can be also considered in terms of quantum electrodynamics.
Standard calculation schemes using perturbation theory have successfully
described particle interaction s involving high -energy photon emission such as
(inverse) Compton scattering. However photon emission under the action of strong
background electromagnetic field is not covered by the perturbation theory since
numerous low energy photons simultaneously con tribute the emission process.
Fortunately a semi -classical approach can be applied for photon emission from
high-energy electron, and we have obtained theoretical cross sections that have a
direct relevance to the synchrotron radiation.
The quantum strong -field theory and related cross sections are characterized by
a covariant quantum parameter [52] [Nik 64] . The quantum parameter
is defined
as
2
22()LLef f F pmc mc mc
(5.4)
where
,
F and
p denote Compton wavelength and field 4 -tensor and 4 –
momentum of electron, respectively. Background field strength affects the cross
section via the parameter. Obtained cross section
qW is as follows:
( , ) ( , ) ( , )q pl deW W W
2
532( ),3 (1 ) 3pldW mcds K sd
(5.5)
2
2312 1)
3 1(pldW mcKd
(5.6)
47
where
and
are fine structure and Plank constants, respectively [59] [Ber 81].
This cross section is given as a function of the ratio of emitted photon energy to
incident electron energy
he , where
h and
e are photon and electron
energies, respect ively.
The ra diation cross section in quantum regime, Eqs. (5.5) and (5.6), is directly
compared with that of synchrotron radiation, Eq. (5.3). By converting photon
frequency
to photon energy ,
h
, the characteristic frequency of
synchrotron radiation is described by the quantum parameter such that
ce .
Then, the intensity of synchrotron radiation is given as a function of
and
.
Resulting classical cross section,
( , )cl clWW , and potential of radiated
electromagnetic field,
clA , relate to the first term of quantum cross section
plW in
Eq. (5.5) [54] [Sok 1 1],
1( , ) (1 ) , , ( , ) ,1 1 1pl cl pl cldW dW A A (5.7)
Thus polarization of this component is evaluated from that of synchrotron radiation
given in Eq. (5.1). On the other hand, the second term,
deW , in Eq. (5.6) comes from
purely quantum effect relevant to electron spin, while the first term is derived from
spin-less QED [53] [Sok 86] . We assume emitted photon associated with this term
is depolarized for incident electrons without a defined polarization.
Quantum effects assoc iated with the second term,
deW , can be examined by
polarization measurements. The first term,
plW , is separated into parallel,
()pl cW ,
and perpendicular,
()pl dW , in the similar manner to the classical cross section in Eq
(5.1). Figure 5.1 shows energy spectrum of these two compone nts and
deW for
=
(A) 0.01 and (B) 0.3. For low
, as shown in panel (A), the contribution of
deW is
small and emitted photons are highly polarized in par allel direction except at the
low energy reg ion with certain value of
()pl dW . This result corresponds to the high
polarization ratio of synchrotron radiation. On the other hand, the contribution of
deW
dominates that of
clW at the high energy region for
= 0.3 as shown in panel
(B). Thus clear consequence of the second term, i.e., quantum effect associated
with electron spin, can be observed in the polarization c omponent of high -energy
photons.
Figure 5.1 – Energy spectrum for polarized and depolarized components for χ = (A) 0.01 and (B)
0.3. Lines indicate Wpl, Wde , ratio of Wpl(c) to Wcl and ratio of Wde to Wq. Ratios are given with respect
to the right side axis.
48
Contributions of
()pl dW and
deW to the perpendicular compo nent tend to be
small in the middle range of energy spectrum. High -energy photons with high
linear polarization ratio would be obtained from this energy range by using linear
polarized pulse laser and high -energy electron beam. Obtained photons are useful
to probe the light -by-light scattering in vacuum.
5.3. Technical Proposal
This experiment is carried out as sub -experiments of RA5 -RR, RA5 -Pair and
RA5 -VBir with the layout of Stage 1.5 and Stage 3. See the detail of these in
sections of RA5 -RR.
5.4. Count Estimat ion
Energy spectrum for parallel and perpendicular polarized components is
examined for head -on collision between pulse laser and accelerated electron bunch.
Employed conditions are relevant to the experimental setup. We consider the
electron beam from acc elerator (LINAC). Initial energy is 600 [MeV] and 109
electrons are included per electron bunch. Bunch size is 15 [μm] in both cases.
Pulse laser is a Gaussian pulse with pulse duration of 22 [fs] and a spot size of 5
[μm]. Laser intensity is 1022 [W/cm2].
We perform a Monte -Carlo simulation to examine the polarization of emitted
photon. Stochastic photon emission is implemented by a Monte -Carlo event
generator according to the quantum cross section ( Eqs. (4.5) and (4.6)). Photon
energy and emission a ngle are recorded to obtain photon energy spectrum and
angle distribution. In addition, we record the degree of linear polarization in the
first term,
plW , Eq. (4.5) and ratio the second term,
deW , Eq. (4.5). Former is
calculated from the polarization ratio of synchrotron radiation Eq. (4.1)). The
results of simulation indicate that significant portion of photon comes from the
spin-dependent term for ~ 400[MeV] energy range. For classical radiation, degree
of polarization is almost unity in this energy range. Thus we could exam ine the
spin-related QED effects based on the measurement of polarization.
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